How do you convert units to a different measurement? And how do you know how
many decimal places to move as a result? Doctor Ian suggests making the
multiplication of units explicit, and introduces ratios of two quantities equal to each
other.

A student put points P and Q on a line to the right of point X. Three
times the distance from point X to point P is four times the distance
from point X to point Q. What is the ratio of PQ:XQ? The answer key says
1:4.......the class and teacher disagree. What do you say?

A grocer wishes to mix 6 pounds of Chippy dog food worth $3 per pound
with Hippy dog food, worth $4 per pound. How much of the Hippy dog
food should be mixed if the dog food mixture is to sell for $3.20?

If you need 5 lbs of flour to make 10 lbs of batter, how many pounds
of flour do you need for 1 lb of batter? I know how to do this problem
(divide 5 by 10) but I don't understand why dividing the 5 lbs by the
whole (10 lbs) gives you the amount for a SINGLE pound of batter.

In a picture of a person holding a mirror and looking into a mirror, the
image is repeated over and over again. The large picture is made of an
infinite number of smaller pictures, all of which are proportional. The
first image is about 15cm. The second image is about 5.8cm. What is the
actual height of the 10th image in the picture?